Why would a displacement with a periodic image not tile smoothly?
The problem is in the smoothing function. As one surface get's near one edge, it doesn't know how the curvature will continue on the other side and the smoothing function sets it as if the object ends there, using no interpolation between the disconnected edges. This happens from both sides of the common edge, and therefore it's quite noticeable.

To correct this, one must edit the vertex normals from each side, to include the derivation from one surface's normal to the other.
However this might be very tedious to do by hand, so I advise a good normal editor addon. For example, Y.A.V.N.E. has one function for this (the merge normals), and all one need is to join the meshes (if in different objects), select the edge vertices, merge the normals and separate the meshes again (if needed).